In this paper a new posterior odds analysis is proposed to test for a unit root in UnobservedARCH
models. Our analysis extends the Bayesian unit root test of . Also a method for estimating the
probability of the null hypothesis in prior odds ratio is demonstrated. Simulation study shows that
this method is efficient. An empirical study, based on time series data of daily exchange rate of the
German Marc with respect to the Greek Drachma, is applied using this method.